In order to clarify the mechanism of high proton conductivity (sigma(H+)) for superprotonic ionic conductors, MHXO4, where M=Cs and Rb, X=S and Se, muon-spin rotation and relaxation (mu+SR) and quasi-elastic neutron scattering (QENS) measurements have been performed at temperatures mainly in the vicinity of Tc, at which MHXO4 undergoes a structural phase transition from a low-T orthorhombic phase (Phase II) to a high-T tetragonal phase (Phase I). The mu+SR experiment shows the presence of muonium (Mu) state even in Phase I only for CsHSO4 (CHS), while no Mu state was found in Phase I of CsHSeO4 (CHSe). Considering the fact that the sigma(H+) in Phase I of CHS is more than 10 times larger that of CHSe, this implies a relationship between the presence of the atomic hydrogen (Mu) state and high sigma(H+) in Phase I of CHS. According to the QENS measurements using a single crystal of CHSe, line shapes of the energy spectra along three crystallographic directions are found to be slightly anisotropic in Phase I, in contrast to the isotropic conductivity reported by AC conductivity measurements. (C) 2008 Elsevier B.V. All rights reserved.